In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. The theoretical results and empirical results that show the utility of the proposed methods are also provided.
@article{arxiv.1909.02750,
title = {Differentially Private Precision Matrix Estimation},
author = {Wenqing Su and Xiao Guo and Hai Zhang},
journal= {arXiv preprint arXiv:1909.02750},
year = {2019}
}